This polychoron is just an edge-faceting of tetaco.

Incidence matrix according to Dynkin symbol

reduced( xx3/2oo3ox3*a&#x by x.3/2o.3o.3*a )   → height = sqrt(5/8) = 0.790569
(pseudo 2tet || oho)

         o.3/2o.3o.3*a        | 4  * | 3  3  0  0 | 3  6  3 0 0 0 | 3 3 1 0
         .o3/2.o3.o3*a        | * 12 | 0  1  2  2 | 0  2  2 1 2 1 | 1 2 1 1
------------------------------+------+------------+---------------+--------
reduced( x.   .. ..         ) | 2  0 | 6  *  *  * | 2  2  0 0 0 0 | 2 2 0 0
         oo3/2oo3oo3*a&#x     | 1  1 | * 12  *  * | 0  2  2 0 0 0 | 1 2 1 0
         .x   .. ..           | 0  2 | *  * 12  * | 0  1  0 1 1 0 | 1 1 0 1
         ..   .. .x           | 0  2 | *  *  * 12 | 0  0  1 0 1 1 | 0 1 1 1
------------------------------+------+------------+---------------+--------
reduced( x.3/2o. ..       & ) | 3  0 | 3  0  0  0 | 4  *  * * * * | 1 1 0 0
         xx   .. ..   &#x     | 2  2 | 1  2  1  0 | * 12  * * * * | 1 1 0 0
         ..   .. ox   &#x     | 1  2 | 0  2  0  1 | *  * 12 * * * | 0 1 1 0
         .x3/2.o ..           | 0  3 | 0  0  3  0 | *  *  * 4 * * | 1 0 0 1
         .x   .. .x3*a        | 0  6 | 0  0  3  3 | *  *  * * 4 * | 0 1 0 1
         ..   .o3.x           | 0  3 | 0  0  0  3 | *  *  * * * 4 | 0 0 1 1
------------------------------+------+------------+---------------+--------
         xx3/2oo ..   &#x     ♦ 3  3 | 3  3  3  0 | 1  3  0 1 0 0 | 4 * * *
         xx   .. ox3*a&#x     ♦ 3  6 | 3  6  3  3 | 1  3  3 0 1 0 | * 4 * *
         ..   oo3ox   &#x     ♦ 1  3 | 0  3  0  3 | 0  0  3 0 0 1 | * * 4 *
         .x3/2.o3.x           ♦ 0 12 | 0  0 12 12 | 0  0  0 4 4 4 | * * * 1